Environment Preparation and Data Import

Import of relevant Libraries.

Generate functions to be used throughout the analysis.

# Function to automatically calculate effect sizes
effectsizecalculator <-  function (i) {
  esc_mean_sd(grp1m = data$minttc[effectsizes$id_ctrl[i] == data$id],
              grp1sd = data$minttc_sd[effectsizes$id_ctrl[i] == data$id],
              grp1n =  data$sample_size[effectsizes$id_ctrl[i] == data$id],
              grp2m = data$minttc[effectsizes$id_exp[i] == data$id],
              grp2sd = data$minttc_sd[effectsizes$id_exp[i] == data$id],
              grp2n = data$sample_size[effectsizes$id_exp[i] == data$id],
              es.type = 'g',
              study = studies$authors_meta[effectsizes$study_id[i] == studies$id])
}
# Function to locate authors to studies
authors <- function (a) {
  studies$authors[effectsizes$study_id[a] == studies$id]
}

# Function to calculate variance distribution
mlm.variance.distribution = function(x){
  
  m = x
  
  # Check class
  if (!(class(m)[1] %in% c("rma.mv", "rma"))){
    stop("x must be of class 'rma.mv'.")
  }
  
  # Check for three level model
  if (m$sigma2s != 2){
    stop("The model you provided does not seem to be a three-level model. This function can only be used for three-level models.")
  }
  
  # Get variance diagonal and calculate total variance
  n = m$k.eff
  vector.inv.var = 1/(diag(m$V))
  sum.inv.var = sum(vector.inv.var)
  sum.sq.inv.var = (sum.inv.var)^2
  vector.inv.var.sq = 1/(diag(m$V)^2)
  sum.inv.var.sq = sum(vector.inv.var.sq)
  num = (n-1)*sum.inv.var
  den = sum.sq.inv.var - sum.inv.var.sq
  est.samp.var = num/den
  
  # Calculate variance proportions
  level1=((est.samp.var)/(m$sigma2[1]+m$sigma2[2]+est.samp.var)*100)
  level2=((m$sigma2[2])/(m$sigma2[1]+m$sigma2[2]+est.samp.var)*100)
  level3=((m$sigma2[1])/(m$sigma2[1]+m$sigma2[2]+est.samp.var)*100)
  
  # Prepare df for return
  Level=c("Level 1", "Level 2", "Level 3")
  Variance=c(level1, level2, level3)
  df.res=data.frame(Variance)
  colnames(df.res) = c("% of total variance")
  rownames(df.res) = Level
  I2 = c("---", round(Variance[2:3], 2))
  df.res = as.data.frame(cbind(df.res, I2))
  
  totalI2 = Variance[2] + Variance[3]
  
  
  # Generate plot
  df1 = data.frame("Level" = c("Sampling Error", "Total Heterogeneity"),
                   "Variance" = c(df.res[1,1], df.res[2,1]+df.res[3,1]),
                   "Type" = rep(1,2))
  
  df2 = data.frame("Level" = rownames(df.res),
                   "Variance" = df.res[,1],
                   "Type" = rep(2,3))
  
  df = as.data.frame(rbind(df1, df2))
  
  
  g = ggplot(df, aes(fill=Level, y=Variance, x=as.factor(Type))) +
    coord_cartesian(ylim = c(0,1), clip = "off") +
    geom_bar(stat="identity", position="fill", width = 1, color="black") +
    scale_y_continuous(labels = scales::percent)+
    theme(axis.title.x=element_blank(),
          axis.text.y = element_text(color="black"),
          axis.line.y = element_blank(),
          axis.title.y=element_blank(),
          axis.line.x = element_blank(),
          axis.ticks.x = element_blank(),
          axis.text.x = element_blank(),
          axis.ticks.y = element_line(lineend = "round"),
          legend.position = "none",
          panel.grid.major = element_blank(),
          panel.grid.minor = element_blank(),
          panel.background = element_blank(),
          legend.background = element_rect(linetype="solid",
                                           colour ="black"),
          legend.title = element_blank(),
          legend.key.size = unit(0.75,"cm"),
          axis.ticks.length=unit(.25, "cm"),
          plot.margin = unit(c(1,3,1,1), "lines")) +
    scale_fill_manual(values = c("darkseagreen3", "deepskyblue3", "darkseagreen2",
                                 "deepskyblue1", "deepskyblue2")) +
    
    # Add Annotation
    
    # Total Variance
    annotate("text", x = 1.5, y = 1.05,
             label = paste("Total Variance:",
                           round(m$sigma2[1]+m$sigma2[2]+est.samp.var, 3))) +
    
    # Sampling Error
    annotate("text", x = 1, y = (df[1,2]/2+df[2,2])/100,
             label = paste("Sampling Error Variance: \n", round(est.samp.var, 3)), size = 3) +
    
    # Total I2
    annotate("text", x = 1, y = ((df[2,2])/100)/2-0.02,
             label = bquote("Total"~italic(I)^2*":"~.(round(df[2,2],2))*"%"), size = 3) +
    annotate("text", x = 1, y = ((df[2,2])/100)/2+0.05,
             label = paste("Variance not attributable \n to sampling error: \n", round(m$sigma2[1]+m$sigma2[2],3)), size = 3) +
    
    # Level 1
    annotate("text", x = 2, y = (df[1,2]/2+df[2,2])/100, label = paste("Level 1: \n",
                                                                       round(df$Variance[3],2), "%", sep=""), size = 3) +
    
    # Level 2
    annotate("text", x = 2, y = (df[5,2]+(df[4,2]/2))/100,
             label = bquote(italic(I)[Level2]^2*":"~.(round(df[4,2],2))*"%"), size = 3) +
    
    # Level 3
    annotate("text", x = 2, y = (df[5,2]/2)/100,
             label = bquote(italic(I)[Level3]^2*":"~.(round(df[5,2],2))*"%"), size = 3)
  
  print(df.res)
  cat("Total I2: ", round(totalI2, 2), "% \n", sep="")
  suppressWarnings(print(g))
  invisible(df.res)
}

# Automatically spot outliers
spot.outliers.random<-function(data){
  data<-data
  Author<-data$studlab
  lowerci<-data$lower
  upperci<-data$upper 
  m.outliers<-data.frame(Author,lowerci,upperci) 
  te.lower<-data$lower.random 
  te.upper<-data$upper.random 
  dplyr::filter(m.outliers,upperci < te.lower) 
  dplyr::filter(m.outliers,lowerci > te.upper)
}

# Plot hat values
hat.plot <-function(fit) {
    p <- length(coefficients(fit))
    n <- length(fitted(fit))
    plot(hatvalues(fit), main="Index Plot of Hat Values")
    abline(h=c(2,3)*p/n, col="red", lty=2)
    identify(1:n, hatvalues(fit), names(hatvalues(fit)))
}

Import files.

## # A tibble: 6 x 7
##      id authors      authors_meta    year title           type   Source         
##   <dbl> <chr>        <chr>          <dbl> <chr>           <chr>  <chr>          
## 1     1 Feldhütter,… Feldhütter et…  2017 How the Durati… confe… Advances in Er…
## 2     2 Körber, Gol… Körber et al.…  2016 The influence … journ… Transportation…
## 3     3 Gold, Körbe… Gold et al., …  2016 Taking Over Co… journ… Human Factors:…
## 4     4 Wandtner, S… Wandtner et a…  2018 Effects of Non… journ… Human Factors:…
## 5     6 Radlmayr, F… Radlmayr et a…  2019 The Influence … confe… Advances in In…
## 6     7 Wan & Wu     Wan et al., 2…  2018 The Effects of… journ… International …
## # A tibble: 6 x 27
##      id studynr effectsize_id exp_cond exp_cond_descri… ndt_description
##   <dbl>   <dbl> <chr>            <dbl> <chr>            <chr>          
## 1     1       1 1                    1 SuRT             visual, manual 
## 2     2       1 1                    2 No NDT           -              
## 3     3       2 2                    1 Young, No NDT, … -              
## 4     4       2 3                    2 Young, No NDT, … -              
## 5     5       2 4                    3 Young, No NDT, … -              
## 6     6       2 2                    4 Young, NDT, 0 v… acoustic, cogn…
## # … with 21 more variables: subject_group <dbl>, sample_size <dbl>,
## #   minttc <dbl>, minttc_sd <dbl>, mtot <dbl>, mtot_sd <dbl>, age <dbl>,
## #   age_sd <dbl>, sim <chr>, lad <dbl>, ndt_v <chr>, ndt_a <chr>, ndt_m <chr>,
## #   ndt_c <chr>, hand <chr>, ndt_p <chr>, tor_p <chr>, dre <chr>, iru <chr>,
## #   urg <chr>, tbtc <dbl>
## # A tibble: 6 x 27
##      id studynr effectsize_id exp_cond exp_cond_descri… ndt_description
##   <dbl>   <dbl> <chr>            <dbl> <chr>            <chr>          
## 1     1       1 1                    1 SuRT             visual, manual 
## 2     2       1 1                    2 No NDT           -              
## 3     3       2 2                    1 Young, No NDT, … -              
## 4     4       2 3                    2 Young, No NDT, … -              
## 5     5       2 4                    3 Young, No NDT, … -              
## 6     6       2 2                    4 Young, NDT, 0 v… acoustic, cogn…
## # … with 21 more variables: subject_group <dbl>, sample_size <dbl>,
## #   minttc <dbl>, minttc_sd <dbl>, mtot <dbl>, mtot_sd <dbl>, age <dbl>,
## #   age_sd <dbl>, sim <dbl>, lad <dbl>, ndt_v <dbl>, ndt_a <dbl>, ndt_m <dbl>,
## #   ndt_c <dbl>, hand <dbl>, ndt_p <dbl>, tor_p <dbl>, dre <dbl>, iru <dbl>,
## #   urg <dbl>, tbtc <dbl>
## # A tibble: 6 x 10
##   study_id effectsize_id id_exp id_ctrl effect_size standard_error variance
##      <dbl>         <dbl>  <dbl>   <dbl> <lgl>       <lgl>          <lgl>   
## 1        1             1      1       2 NA          NA             NA      
## 2        2             2      6       3 NA          NA             NA      
## 3        2             3      7       4 NA          NA             NA      
## 4        2             4      8       5 NA          NA             NA      
## 5        2             5     12       9 NA          NA             NA      
## 6        2             6     13      10 NA          NA             NA      
## # … with 3 more variables: lower_CI <lgl>, upper_CI <lgl>, weight <lgl>

Effectsize Calculation

Calculate effect sizes for the studies.

Change effectsizes columns to numeric.

Merge effectsizs with studies for details.

Merge effectsizes with data for moderators.

Remove unnecessary columns from dataframe.

Rename column(s).

Show output of new effectsizes dataframe.

## 'data.frame':    35 obs. of  37 variables:
##  $ study_id            : num  1 2 2 2 2 2 2 3 3 3 ...
##  $ effectsize_id       : num  1 2 3 4 5 6 7 8 9 10 ...
##  $ effect_size         : num  0.76 0.269 0.571 0.516 1.127 ...
##  $ standard_error      : num  0.402 0.335 0.34 0.339 0.36 ...
##  $ variance            : num  0.161 0.112 0.116 0.115 0.13 ...
##  $ lower_CI            : num  -0.027 -0.3875 -0.0959 -0.1486 0.4212 ...
##  $ upper_CI            : num  1.548 0.925 1.238 1.181 1.832 ...
##  $ weight              : num  6.2 8.92 8.63 8.7 7.72 ...
##  $ totaln              : num  27 36 36 36 36 36 36 71 71 71 ...
##  $ measure             : chr  "g" "g" "g" "g" ...
##  $ study               : chr  "Feldhütter et al., 2017" "Körber et al., 2016" "Körber et al., 2016" "Körber et al., 2016" ...
##  $ year                : num  2017 2016 2016 2016 2016 ...
##  $ title               : chr  "How the Duration of Automated Driving Influences Take-Over Performance and Gaze Behavior" "The influence of age on the take-over of vehicle control in highly automated driving" "The influence of age on the take-over of vehicle control in highly automated driving" "The influence of age on the take-over of vehicle control in highly automated driving" ...
##  $ type                : chr  "conference paper" "journal article" "journal article" "journal article" ...
##  $ Source              : chr  "Advances in Ergonomic Design of Systems, Products and Processes" "Transportation Research Part F: Traffic Psychology and Behaviour" "Transportation Research Part F: Traffic Psychology and Behaviour" "Transportation Research Part F: Traffic Psychology and Behaviour" ...
##  $ exp_cond_description: chr  "SuRT" "Young, NDT, 0 vehicle/km" "Young, NDT, 10 vehicle/km" "Young, NDT, 20 vehicle/km" ...
##  $ ndt_description     : chr  "visual, manual" "acoustic, cognitive" "acoustic, cognitive" "acoustic, cognitive" ...
##  $ sample_size         : num  12 18 18 18 18 18 18 35 35 35 ...
##  $ minttc              : num  2.31 2.46 1.56 1.3 2.61 ...
##  $ minttc_sd           : num  0.745 0.512 0.564 0.611 0.66 0.475 0.572 1.17 1.03 1.17 ...
##  $ mtot                : num  2.25 2.76 3.7 3.66 2.62 ...
##  $ mtot_sd             : num  0.855 0.88 0.97 1.24 1.29 1.41 1.1 1.09 1.22 1.14 ...
##  $ age                 : num  24.2 23.3 23.3 23.3 66.7 ...
##  $ age_sd              : num  2.09 2.6 2.6 2.6 4.56 4.56 4.56 22.2 22.2 22.2 ...
##  $ sim                 : Factor w/ 3 levels "high fidelity",..: 3 3 3 3 3 3 3 3 3 3 ...
##  $ lad                 : Factor w/ 2 levels "0","1": 2 2 2 2 2 2 2 2 2 2 ...
##  $ ndt_v               : Factor w/ 2 levels "no","yes": 2 1 1 1 1 1 1 1 1 1 ...
##  $ ndt_a               : Factor w/ 2 levels "no","yes": 1 2 2 2 2 2 2 2 2 2 ...
##  $ ndt_m               : Factor w/ 2 levels "no","yes": 2 1 1 1 1 1 1 1 1 1 ...
##  $ ndt_c               : Factor w/ 2 levels "no","yes": 1 2 2 2 2 2 2 2 2 2 ...
##  $ hand                : Factor w/ 2 levels "no","yes": 1 1 1 1 1 1 1 1 1 1 ...
##  $ ndt_p               : Factor w/ 2 levels "no","yes": 2 2 2 2 2 2 2 2 2 2 ...
##  $ tor_p               : Factor w/ 1 level "yes": 1 1 1 1 1 1 1 1 1 1 ...
##  $ dre                 : Factor w/ 2 levels "high","medium": 2 2 2 2 2 2 2 2 2 2 ...
##  $ iru                 : Factor w/ 2 levels "no","yes": 1 1 2 2 1 2 2 1 2 2 ...
##  $ urg                 : Factor w/ 3 levels "high","low","medium": 1 1 1 1 1 1 1 1 1 1 ...
##  $ tbtc                : num  6 7 7 7 7 7 7 7 7 7 ...

print a copy of the effectsizes dataframe.

Descriptive Statistics

Descriptive statstics summary

##        id            studynr       effectsize_id      exp_cond     
##  Min.   :  1.00   Min.   : 1.000   Min.   : 1.00   Min.   : 1.000  
##  1st Qu.: 14.75   1st Qu.: 2.750   1st Qu.: 7.00   1st Qu.: 2.000  
##  Median : 64.50   Median : 6.000   Median :45.00   Median : 4.000  
##  Mean   : 52.29   Mean   : 6.036   Mean   :33.98   Mean   : 4.234  
##  3rd Qu.: 78.25   3rd Qu.: 8.000   3rd Qu.:58.00   3rd Qu.: 6.000  
##  Max.   :110.00   Max.   :12.000   Max.   :74.00   Max.   :12.000  
##                                    NA's   :7       NA's   :9       
##  exp_cond_description ndt_description    subject_group    sample_size   
##  Length:56            Length:56          Min.   :1.000   Min.   :12.00  
##  Class :character     Class :character   1st Qu.:1.000   1st Qu.:18.00  
##  Mode  :character     Mode  :character   Median :1.000   Median :36.00  
##                                          Mean   :1.464   Mean   :32.54  
##                                          3rd Qu.:2.000   3rd Qu.:39.00  
##                                          Max.   :4.000   Max.   :49.00  
##                                                                         
##      minttc          minttc_sd           mtot          mtot_sd      
##  Min.   : 0.4375   Min.   :0.0870   Min.   :1.125   Min.   :0.2400  
##  1st Qu.: 1.5295   1st Qu.:0.5507   1st Qu.:1.833   1st Qu.:0.4250  
##  Median : 2.3315   Median :0.7345   Median :2.278   Median :0.8123  
##  Mean   : 3.6273   Mean   :1.3714   Mean   :2.440   Mean   :0.8025  
##  3rd Qu.: 4.0499   3rd Qu.:1.1425   3rd Qu.:3.195   3rd Qu.:1.1200  
##  Max.   :12.4960   Max.   :7.7600   Max.   :3.700   Max.   :1.4400  
##                                     NA's   :1       NA's   :1       
##       age            age_sd                    sim     lad    ndt_v    ndt_a   
##  Min.   :23.28   Min.   : 2.090   high fidelity  : 5   0:12   no :33   no :42  
##  1st Qu.:25.73   1st Qu.: 4.560   low fidelity   : 6   1:44   yes:23   yes:14  
##  Median :31.23   Median : 6.380   medium fidelity:45                           
##  Mean   :37.19   Mean   : 7.527                                                
##  3rd Qu.:45.00   3rd Qu.: 7.100                                                
##  Max.   :71.18   Max.   :22.200                                                
##  NA's   :1       NA's   :4                                                     
##  ndt_m    ndt_c     hand    ndt_p    tor_p        dre      iru         urg    
##  no :48   no :46   no :49   no :21   yes:56   high  :13   no :22   high  :42  
##  yes: 8   yes:10   yes: 7   yes:35            medium:43   yes:34   low   : 8  
##                                                                    medium: 6  
##                                                                               
##                                                                               
##                                                                               
##                                                                               
##       tbtc       
##  Min.   : 3.000  
##  1st Qu.: 6.000  
##  Median : 7.000  
##  Mean   : 8.357  
##  3rd Qu.: 7.750  
##  Max.   :20.000  
## 

Histograms

Correlation matrices

Pearson correlation

##             minttc       ndt_v       ndt_a       ndt_m       ndt_c        hand
## minttc  1.00000000  0.07000871 -0.30620395 -0.21934296 -0.25659431 -0.23232672
## ndt_v   0.07000871  1.00000000 -0.23052136  0.38528033 -0.38924947  0.34298103
## ndt_a  -0.30620395 -0.23052136  1.00000000 -0.23570226  0.80757285 -0.09352195
## ndt_m  -0.21934296  0.38528033 -0.23570226  1.00000000 -0.19034675  0.61721340
## ndt_c  -0.25659431 -0.38924947  0.80757285 -0.19034675  1.00000000 -0.17622684
## hand   -0.23232672  0.34298103 -0.09352195  0.61721340 -0.17622684  1.00000000
## ndt_p  -0.16550810  0.64666979  0.44721360  0.31622777  0.36115756  0.29277002
## dre     0.03814629  0.31472198 -0.21977383 -0.10360238 -0.25636488 -0.07993097
## iru    -0.38025321 -0.07166747  0.12666010  0.01492704  0.08864896 -0.13819750
## urg    -0.72899178 -0.19873812  0.25630730  0.08054961  0.25298389 -0.09321806
##              ndt_p         dre         iru         urg
## minttc -0.16550810  0.03814629 -0.38025321 -0.72899178
## ndt_v   0.64666979  0.31472198 -0.07166747 -0.19873812
## ndt_a   0.44721360 -0.21977383  0.12666010  0.25630730
## ndt_m   0.31622777 -0.10360238  0.01492704  0.08054961
## ndt_c   0.36115756 -0.25636488  0.08864896  0.25298389
## hand    0.29277002 -0.07993097 -0.13819750 -0.09321806
## ndt_p   1.00000000  0.07644455  0.05664412  0.03820804
## dre     0.07644455  1.00000000  0.44229225  0.29833845
## iru     0.05664412  0.44229225  1.00000000  0.67452786
## urg     0.03820804  0.29833845  0.67452786  1.00000000

Spearman correlation

##              minttc       ndt_v       ndt_a       ndt_m       ndt_c        hand
## minttc  1.000000000 -0.07410923 -0.22835664 -0.19101569 -0.21491000 -0.30065935
## ndt_v  -0.074109234  1.00000000 -0.23052136  0.38528033 -0.38924947  0.34298103
## ndt_a  -0.228356640 -0.23052136  1.00000000 -0.23570226  0.80757285 -0.09352195
## ndt_m  -0.191015687  0.38528033 -0.23570226  1.00000000 -0.19034675  0.61721340
## ndt_c  -0.214910002 -0.38924947  0.80757285 -0.19034675  1.00000000 -0.17622684
## hand   -0.300659355  0.34298103 -0.09352195  0.61721340 -0.17622684  1.00000000
## ndt_p  -0.252172591  0.64666979  0.44721360  0.31622777  0.36115756  0.29277002
## dre     0.007850451  0.31472198 -0.21977383 -0.10360238 -0.25636488 -0.07993097
## iru    -0.322361626 -0.07166747  0.12666010  0.01492704  0.08864896 -0.13819750
## urg    -0.298769282 -0.24598667  0.24917096  0.03333333  0.26648545 -0.20720736
##               ndt_p          dre         iru          urg
## minttc -0.252172591  0.007850451 -0.32236163 -0.298769282
## ndt_v   0.646669791  0.314721976 -0.07166747 -0.245986671
## ndt_a   0.447213595 -0.219773831  0.12666010  0.249170961
## ndt_m   0.316227766 -0.103602377  0.01492704  0.033333333
## ndt_c   0.361157559 -0.256364882  0.08864896  0.266485446
## hand    0.292770022 -0.079930969 -0.13819750 -0.207207356
## ndt_p   1.000000000  0.076444546  0.05664412  0.003011693
## dre     0.076444546  1.000000000  0.44229225  0.314260545
## iru     0.056644118  0.442292251  1.00000000  0.710526906
## urg     0.003011693  0.314260545  0.71052691  1.000000000

Scatterplots

Scatterplot of minTTC and minTTC standard deviation

Scatterplot of and mTOT and mTOT standard deviation

## Warning: Removed 1 rows containing missing values (geom_point).

Scatterplot of meanTOT and minTTC

## Warning: Removed 1 rows containing missing values (geom_point).

Scatterplot of meanTOT and minTTC with a fitted least squares line

## `geom_smooth()` using formula 'y ~ x'
## Warning: Removed 1 rows containing non-finite values (stat_smooth).
## Warning: Removed 1 rows containing missing values (geom_point).

Scatterplot of TBTB and minTTC

Scatterplot of TBTC and minTTC with a fitted least squares line

Group comparisons

Group Comparisons for the dependent variable minTTC

##   ndt_p   minttc minttc_sd freq
## 1    no 4.307712  1.715878   21
## 2   yes 3.219092  1.164652   35
##   ndt_v   minttc minttc_sd freq
## 1    no 3.441214  1.335237   33
## 2   yes 3.894353  1.423194   23
##   ndt_a   minttc minttc_sd freq
## 1    no 4.190265 1.6022124   42
## 2   yes 1.938503 0.6788112   14
##   ndt_m   minttc minttc_sd freq
## 1    no 3.912466 1.5079731   48
## 2   yes 1.916476 0.5516965    8
##   ndt_c   minttc minttc_sd freq
## 1    no 4.008286 1.5084548   46
## 2   yes 1.874904 0.7407357   10
##   hand   minttc minttc_sd freq
## 1   no 3.906941  1.478230   49
## 2  yes 1.670010  0.623289    7
##      urg    minttc minttc_sd freq
## 1   high  2.664980  0.699459   42
## 2    low 10.340125  5.342375    8
## 3 medium  1.413333  0.780000    6
##      dre   minttc minttc_sd freq
## 1   high 3.848241 0.8312336   13
## 2 medium 3.560536 1.5346568   43
##   iru   minttc minttc_sd freq
## 1  no 5.132591 2.4351364   22
## 2 yes 2.653329 0.6830376   34

Group Comparisons for mTOT

##   ndt_p     mtot   mtot_sd freq
## 1    no 2.252643 0.8036511   21
## 2   yes 2.546419 0.8017740   35
##   ndt_v     mtot   mtot_sd freq
## 1    no 2.502813 0.8866890   33
## 2   yes 2.351632 0.6852637   23
##   ndt_a     mtot   mtot_sd freq
## 1    no 2.299061 0.7363836   42
## 2   yes 2.851147 0.9959558   14
##   ndt_m     mtot   mtot_sd freq
## 1    no 2.452222 0.7991150   48
## 2   yes 2.365390 0.8220884    8
##   ndt_c     mtot   mtot_sd freq
## 1    no 2.291669 0.7380329   46
## 2   yes 3.105242 1.0923630   10
##   hand     mtot   mtot_sd freq
## 1   no 2.397528 0.7855185   49
## 2  yes 2.728025 0.9186033    7
##      urg     mtot   mtot_sd freq
## 1   high 2.442964 0.8294417   42
## 2    low 1.924500 0.4260000    8
## 3 medium 3.103333 1.1200000    6
##      dre     mtot   mtot_sd freq
## 1   high 1.742769 0.4050000   13
## 2 medium 2.655275 0.9254788   43
##   iru     mtot   mtot_sd freq
## 1  no 2.440727 0.8176364   22
## 2 yes 2.438834 0.7923367   34

Mean difference in minTTC (s) between “NDT” and “no NDT” condition

Mean difference in mTOT (s) between “NDT” and “no NDT” condition

##        id            studynr       effectsize_id      exp_cond     
##  Min.   :  1.00   Min.   : 1.000   Min.   : 1.00   Min.   : 1.000  
##  1st Qu.: 14.75   1st Qu.: 2.750   1st Qu.: 7.00   1st Qu.: 2.000  
##  Median : 64.50   Median : 6.000   Median :45.00   Median : 4.000  
##  Mean   : 52.29   Mean   : 6.036   Mean   :33.98   Mean   : 4.234  
##  3rd Qu.: 78.25   3rd Qu.: 8.000   3rd Qu.:58.00   3rd Qu.: 6.000  
##  Max.   :110.00   Max.   :12.000   Max.   :74.00   Max.   :12.000  
##                                    NA's   :7       NA's   :9       
##  exp_cond_description ndt_description    subject_group    sample_size   
##  Length:56            Length:56          Min.   :1.000   Min.   :12.00  
##  Class :character     Class :character   1st Qu.:1.000   1st Qu.:18.00  
##  Mode  :character     Mode  :character   Median :1.000   Median :36.00  
##                                          Mean   :1.464   Mean   :32.54  
##                                          3rd Qu.:2.000   3rd Qu.:39.00  
##                                          Max.   :4.000   Max.   :49.00  
##                                                                         
##      minttc          minttc_sd           mtot          mtot_sd      
##  Min.   : 0.4375   Min.   :0.0870   Min.   :1.125   Min.   :0.2400  
##  1st Qu.: 1.5295   1st Qu.:0.5507   1st Qu.:1.833   1st Qu.:0.4250  
##  Median : 2.3315   Median :0.7345   Median :2.278   Median :0.8123  
##  Mean   : 3.6273   Mean   :1.3714   Mean   :2.440   Mean   :0.8025  
##  3rd Qu.: 4.0499   3rd Qu.:1.1425   3rd Qu.:3.195   3rd Qu.:1.1200  
##  Max.   :12.4960   Max.   :7.7600   Max.   :3.700   Max.   :1.4400  
##                                     NA's   :1       NA's   :1       
##       age            age_sd                    sim     lad    ndt_v    ndt_a   
##  Min.   :23.28   Min.   : 2.090   high fidelity  : 5   0:12   no :33   no :42  
##  1st Qu.:25.73   1st Qu.: 4.560   low fidelity   : 6   1:44   yes:23   yes:14  
##  Median :31.23   Median : 6.380   medium fidelity:45                           
##  Mean   :37.19   Mean   : 7.527                                                
##  3rd Qu.:45.00   3rd Qu.: 7.100                                                
##  Max.   :71.18   Max.   :22.200                                                
##  NA's   :1       NA's   :4                                                     
##  ndt_m    ndt_c     hand    ndt_p    tor_p        dre      iru         urg    
##  no :48   no :46   no :49   no :21   yes:56   high  :13   no :22   high  :42  
##  yes: 8   yes:10   yes: 7   yes:35            medium:43   yes:34   low   : 8  
##                                                                    medium: 6  
##                                                                               
##                                                                               
##                                                                               
##                                                                               
##       tbtc       
##  Min.   : 3.000  
##  1st Qu.: 6.000  
##  Median : 7.000  
##  Mean   : 8.357  
##  3rd Qu.: 7.750  
##  Max.   :20.000  
## 

Two-Level meta-analytic Model

Build a two-level model whose results then can be compared to the three-level model.

## 
## Random-Effects Model (k = 35; tau^2 estimator: REML)
## 
## tau^2 (estimated amount of total heterogeneity): 0.689 (SE = 0.185)
## tau (square root of estimated tau^2 value):      0.830
## I^2 (total heterogeneity / total variability):   91.30%
## H^2 (total variability / sampling variability):  11.50
## 
## Test for Heterogeneity:
## Q(df = 34) = 333.768, p-val < .001
## 
## Model Results:
## 
## estimate     se   zval   pval  ci.lb  ci.ub 
##    0.329  0.148  2.225  0.026  0.039  0.619  * 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##        estimate  ci.lb  ci.ub 
## tau^2     0.689  0.430  1.281 
## tau       0.830  0.656  1.132 
## I^2(%)   91.302 86.768 95.125 
## H^2      11.497  7.557 20.514

Three-Level meta-analytic Model

Intercept-Only Model

Estimate the overall effect by fitting an intercept-only model.

## 
## Multivariate Meta-Analysis Model (k = 35; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -44.096    88.192    94.192    98.771    94.992   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.689  0.830     35     no  effectsize_id 
## sigma^2.2  0.000  0.000      9     no       study_id 
## 
## Test for Heterogeneity:
## Q(df = 34) = 333.768, p-val < .001
## 
## Model Results:
## 
## estimate     se   tval   pval  ci.lb  ci.ub 
##    0.329  0.148  2.225  0.033  0.028  0.629  * 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

The estimated effect is the same as for the two-level model, but the confidence intervals differ.

Variance Distribution

Determine how the total variance is distributed over the three levels of the meta-analytic model. Print the results in percentages on screen.

## [1] 8.697861
## [1] 91.30214
## [1] 0.0000001483077
##         % of total variance   I2
## Level 1     8.6978606518637  ---
## Level 2    91.3021391998285 91.3
## Level 3     0.0000001483077    0
## Total I2: 91.3%

Calculation of the Intraclass Correlation (ICC)

ICC describes how strongly units in the same group resemble each other.

## [1] 0

ICC = 0 indicates, that the values within clusters (=studies) are not similar. Because of the underlying research question, this was to be expected.

Profile Likelihood Plot

σ_1^2 (variance at the effectsize level) and σ_2^2 (variance at the study level) were fixed at different values. For each value of σ_1^2 and σ_2^2, the likelihood over the remaining model parameters, such as the fixed effects, was estimated. This means it was estimated how likely the values of these parameters are given the observed data. Less negative values of the logarithm indicate a higher likelihood than more negative values.

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The likelihood are highest for the values of σ_1^2 and σ_2^2 that had been estimated in the original model. Since profiling for variance components is done for non-negative value of the variance, the line is highest at this point in the second plot. We can be “fairly confident” that our meta-analytic models could identify the variance components (Viechtbauer, 2017).

Confidence Intervals for Variance

## 
##           estimate  ci.lb  ci.ub 
## sigma^2.1   0.6890 0.4095 1.2176 
## sigma.1     0.8301 0.6399 1.1034 
## 
##           estimate  ci.lb  ci.ub 
## sigma^2.2   0.0000 0.0000 0.2900 
## sigma.2     0.0000 0.0000 0.5385

The confindence intervals are very wide. For 𝜎22 hence, while the most likely value is 0, other values above 0 cannot be rejected either.

Two-Level Model without within-study variance

Build a two-level model without within-study variance.

## 
## Multivariate Meta-Analysis Model (k = 35; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
## -144.225   288.450   292.450   295.503   292.837   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.000  0.000     35    yes  effectsize_id 
## sigma^2.2  0.059  0.244      9     no       study_id 
## 
## Test for Heterogeneity:
## Q(df = 34) = 333.768, p-val < .001
## 
## Model Results:
## 
## estimate     se   tval   pval  ci.lb  ci.ub 
##    0.315  0.097  3.264  0.003  0.119  0.511  ** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Perform a likelihood-ratio-test to determine the significance of the within-study (level 2) variance.

## 
##         df      AIC      BIC     AICc    logLik      LRT   pval       QE 
## Full     3  94.1919  98.7710  94.9919  -44.0960                 333.7676 
## Reduced  2 292.4499 295.5026 292.8370 -144.2249 200.2579 <.0001 333.7676

The model does not perform better than the three-level model.

Two-level model without between-study variance

Build a two-level model without between-study variance.

## 
## Multivariate Meta-Analysis Model (k = 35; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -44.096    88.192    92.192    95.245    92.579   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.689  0.830     35     no  effectsize_id 
## sigma^2.2  0.000  0.000      9    yes       study_id 
## 
## Test for Heterogeneity:
## Q(df = 34) = 333.768, p-val < .001
## 
## Model Results:
## 
## estimate     se   tval   pval  ci.lb  ci.ub 
##    0.329  0.148  2.225  0.033  0.028  0.629  * 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Perform a likelihood-ratio-test to determine the significance of the between-study (level 3) variance.

## 
##         df     AIC     BIC    AICc   logLik    LRT   pval       QE 
## Full     3 94.1919 98.7710 94.9919 -44.0960               333.7676 
## Reduced  2 92.1919 95.2447 92.5790 -44.0960 0.0000 1.0000 333.7676

This model does perform very similar to the three-level model. A third model for modeling differences between studies is not needed.

Moderator Analysis

NDT Modality

Test of different modalities independently

— acoustic NDT

## 
## Multivariate Meta-Analysis Model (k = 35; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -43.300    86.599    92.599    97.089    93.427   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.713  0.844     35     no  effectsize_id 
## sigma^2.2  0.000  0.000      9    yes       study_id 
## 
## Test for Residual Heterogeneity:
## QE(df = 33) = 333.302, p-val < .001
## 
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 33) = 0.002, p-val = 0.969
## 
## Model Results:
## 
##           estimate     se    tval   pval   ci.lb  ci.ub 
## intrcpt      0.334  0.193   1.731  0.093  -0.058  0.726  . 
## ndt_ayes    -0.012  0.307  -0.039  0.969  -0.637  0.613    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

— manual NDT

## 
## Multivariate Meta-Analysis Model (k = 35; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -42.849    85.697    91.697    96.187    92.525   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.694  0.833     35     no  effectsize_id 
## sigma^2.2  0.000  0.000      9    yes       study_id 
## 
## Test for Residual Heterogeneity:
## QE(df = 33) = 331.804, p-val < .001
## 
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 33) = 0.901, p-val = 0.350
## 
## Model Results:
## 
##           estimate     se   tval   pval   ci.lb  ci.ub 
## intrcpt      0.254  0.168  1.507  0.141  -0.089  0.596    
## ndt_myes     0.338  0.357  0.949  0.350  -0.387  1.064    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

— cognitive NDT

## 
## Multivariate Meta-Analysis Model (k = 35; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -43.137    86.274    92.274    96.763    93.101   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.705  0.840     35     no  effectsize_id 
## sigma^2.2  0.000  0.000      9    yes       study_id 
## 
## Test for Residual Heterogeneity:
## QE(df = 33) = 330.616, p-val < .001
## 
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 33) = 0.317, p-val = 0.577
## 
## Model Results:
## 
##           estimate     se   tval   pval   ci.lb  ci.ub 
## intrcpt      0.277  0.176  1.576  0.125  -0.081  0.635    
## ndt_cyes     0.188  0.334  0.563  0.577  -0.491  0.866    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

— visual NDT

## 
## Multivariate Meta-Analysis Model (k = 35; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -43.151    86.303    92.303    96.792    93.130   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.707  0.841     35     no  effectsize_id 
## sigma^2.2  0.000  0.000      9    yes       study_id 
## 
## Test for Residual Heterogeneity:
## QE(df = 33) = 332.635, p-val < .001
## 
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 33) = 0.290, p-val = 0.594
## 
## Model Results:
## 
##           estimate     se   tval   pval   ci.lb  ci.ub 
## intrcpt      0.215  0.259  0.830  0.413  -0.312  0.742    
## ndt_vyes     0.171  0.317  0.539  0.594  -0.475  0.817    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

—handheld NDT

## 
## Multivariate Meta-Analysis Model (k = 35; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -42.923    85.846    91.846    96.336    92.674   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.698  0.835     35     no  effectsize_id 
## sigma^2.2  0.000  0.000      9    yes       study_id 
## 
## Test for Residual Heterogeneity:
## QE(df = 33) = 331.826, p-val < .001
## 
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 33) = 0.767, p-val = 0.388
## 
## Model Results:
## 
##          estimate     se   tval   pval   ci.lb  ci.ub 
## intrcpt     0.264  0.166  1.588  0.122  -0.074  0.602    
## handyes     0.325  0.372  0.876  0.388  -0.431  1.082    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

All task modalities in one model.

## 
## Multivariate Meta-Analysis Model (k = 35; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -36.163    72.326    86.326    95.897    91.659   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.626  0.791     35     no  effectsize_id 
## sigma^2.2  0.000  0.000      9    yes       study_id 
## 
## Test for Residual Heterogeneity:
## QE(df = 29) = 283.692, p-val < .001
## 
## Test of Moderators (coefficients 2:6):
## F(df1 = 5, df2 = 29) = 1.705, p-val = 0.165
## 
## Model Results:
## 
##           estimate     se    tval   pval   ci.lb   ci.ub 
## intrcpt     -1.479  0.709  -2.087  0.046  -2.929  -0.030  * 
## ndt_ayes     0.135  0.506   0.266  0.792  -0.900   1.169    
## ndt_myes     0.417  0.458   0.910  0.370  -0.520   1.354    
## ndt_cyes     1.809  0.721   2.509  0.018   0.335   3.283  * 
## ndt_vyes     1.638  0.669   2.449  0.021   0.270   3.006  * 
## handyes      0.333  0.447   0.745  0.462  -0.581   1.248    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Urgency

One-hot encoding of urgency.

Determine the potential moderating effect of urgency as categorical moderator. Low urgency is chosen as the reference category.

## 
## Multivariate Meta-Analysis Model (k = 35; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -42.364    84.727    92.727    98.590    94.209   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.731  0.855     35     no  effectsize_id 
## sigma^2.2  0.000  0.000      9    yes       study_id 
## 
## Test for Residual Heterogeneity:
## QE(df = 32) = 326.517, p-val < .001
## 
## Test of Moderators (coefficients 2:3):
## F(df1 = 2, df2 = 32) = 0.152, p-val = 0.859
## 
## Model Results:
## 
##             estimate     se    tval   pval   ci.lb  ci.ub 
## intrcpt        0.351  0.443   0.792  0.434  -0.552  1.253    
## urg_medium     0.175  0.595   0.295  0.770  -1.037  1.387    
## urg_high      -0.064  0.477  -0.134  0.894  -1.036  0.908    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Determine the potential moderating effect of urgency as continuous moderator. High urgency is chosen as intercept category.

## 
## Multivariate Meta-Analysis Model (k = 35; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -42.364    84.727    92.727    98.590    94.209   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.731  0.855     35     no  effectsize_id 
## sigma^2.2  0.000  0.000      9    yes       study_id 
## 
## Test for Residual Heterogeneity:
## QE(df = 32) = 326.517, p-val < .001
## 
## Test of Moderators (coefficients 2:3):
## F(df1 = 2, df2 = 32) = 0.152, p-val = 0.859
## 
## Model Results:
## 
##            estimate     se   tval   pval   ci.lb  ci.ub 
## intrcpt       0.287  0.177  1.621  0.115  -0.074  0.647    
## urglow        0.064  0.477  0.134  0.894  -0.908  1.036    
## urgmedium     0.239  0.435  0.550  0.586  -0.647  1.125    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Determine the potential moderating effect of time budget to collision.

## 
## Multivariate Meta-Analysis Model (k = 35; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -43.264    86.528    92.528    97.017    93.355   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.711  0.843     35     no  effectsize_id 
## sigma^2.2  0.000  0.000      9    yes       study_id 
## 
## Test for Residual Heterogeneity:
## QE(df = 33) = 331.490, p-val < .001
## 
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 33) = 0.106, p-val = 0.747
## 
## Model Results:
## 
##          estimate     se   tval   pval   ci.lb  ci.ub 
## intrcpt     0.247  0.293  0.842  0.406  -0.350  0.844    
## tbtc        0.010  0.031  0.325  0.747  -0.054  0.074    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Exploratory Moderator Analyses

Simulator Fidelity

## 
## Multivariate Meta-Analysis Model (k = 35; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -41.697    83.394    91.394    97.257    92.876   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.702  0.838     35     no  effectsize_id 
## sigma^2.2  0.000  0.000      9    yes       study_id 
## 
## Test for Residual Heterogeneity:
## QE(df = 32) = 322.433, p-val < .001
## 
## Test of Moderators (coefficients 2:3):
## F(df1 = 2, df2 = 32) = 0.813, p-val = 0.453
## 
## Model Results:
## 
##                     estimate     se    tval   pval   ci.lb  ci.ub 
## intrcpt                0.775  0.447   1.735  0.092  -0.135  1.685  . 
## simlow fidelity       -0.249  0.593  -0.420  0.677  -1.457  0.959    
## simmedium fidelity    -0.552  0.479  -1.152  0.258  -1.528  0.424    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Driver response complexity

## 
## Multivariate Meta-Analysis Model (k = 35; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -42.306    84.613    90.613    95.102    91.440   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.666  0.816     35     no  effectsize_id 
## sigma^2.2  0.000  0.000      9    yes       study_id 
## 
## Test for Residual Heterogeneity:
## QE(df = 33) = 315.691, p-val < .001
## 
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 33) = 2.079, p-val = 0.159
## 
## Model Results:
## 
##            estimate     se    tval   pval   ci.lb  ci.ub 
## intrcpt      -0.019  0.282  -0.067  0.947  -0.592  0.554    
## dremedium     0.474  0.329   1.442  0.159  -0.195  1.144    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Interaction with other road users

## 
## Multivariate Meta-Analysis Model (k = 35; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -42.933    85.866    91.866    96.356    92.694   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.694  0.833     35     no  effectsize_id 
## sigma^2.2  0.000  0.000      9    yes       study_id 
## 
## Test for Residual Heterogeneity:
## QE(df = 33) = 323.312, p-val < .001
## 
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 33) = 0.751, p-val = 0.392
## 
## Model Results:
## 
##          estimate     se    tval   pval   ci.lb  ci.ub 
## intrcpt     0.496  0.243   2.041  0.049   0.002  0.990  * 
## iruyes     -0.266  0.307  -0.867  0.392  -0.890  0.358    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Level of Automated Driving

## 
## Multivariate Meta-Analysis Model (k = 35; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -43.316    86.632    92.632    97.121    93.459   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.714  0.845     35     no  effectsize_id 
## sigma^2.2  0.000  0.000      9    yes       study_id 
## 
## Test for Residual Heterogeneity:
## QE(df = 33) = 333.557, p-val < .001
## 
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 33) = 0.001, p-val = 0.980
## 
## Model Results:
## 
##          estimate     se   tval   pval   ci.lb  ci.ub 
## intrcpt     0.322  0.330  0.975  0.337  -0.350  0.994    
## lad1        0.009  0.371  0.025  0.980  -0.745  0.764    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Publication Bias

Visualization: Funnel Plot

Simple funnel plot.

Contour-enhanced funnel plot.

Contour-enhanced sunset funnel plot estimating the power of studies.

Trim-and-fill method

This is a non-parametric approach, where pseudo-studies are being imputed until the funnel plot symmetry is restored.

## 
## Estimated number of missing studies on the left side: 10 (SE = 3.8535)
## 
## Random-Effects Model (k = 45; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
## -64.7588  129.5176  133.5176  137.0860  133.8103   
## 
## tau^2 (estimated amount of total heterogeneity): 1.0060 (SE = 0.2313)
## tau (square root of estimated tau^2 value):      1.0030
## I^2 (total heterogeneity / total variability):   93.71%
## H^2 (total variability / sampling variability):  15.90
## 
## Test for Heterogeneity:
## Q(df = 44) = 565.7152, p-val < .0001
## 
## Model Results:
## 
## estimate      se    zval    pval    ci.lb   ci.ub 
##   0.0060  0.1553  0.0384  0.9694  -0.2985  0.3104    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Testing the results of the the trim-and-fill method for the three-level model against the two-level model

No differences in the results can be detected.

Egger Regression Symmetry Test

Test for asymmetry of the funnel plot. It tests for the Y intercept = 0 from a linear regression of normalized effect estimate.

## 
## Multivariate Meta-Analysis Model (k = 35; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -42.372    84.744    92.744    98.730    94.172   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.000  0.000      9     no       study_id 
## sigma^2.2  0.674  0.821     35     no  effectsize_id 
## 
## Test for Residual Heterogeneity:
## QE(df = 33) = 325.381, p-val < .001
## 
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 33) = 1.872, p-val = 0.180
## 
## Model Results:
## 
##          estimate     se    tval   pval   ci.lb  ci.ub 
## intrcpt    -0.597  0.692  -0.862  0.395  -2.005  0.811    
## mods        3.433  2.509   1.368  0.180  -1.672  8.537    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

The p-value is > 0.05, which indicates non-existence of publication bias.

Rank-Correlation Test

Correlates the standardized treatment effect with the variance of the treatment effect using Kendall’s tau as the measure of association. Since it is not available for three-level meta-analysis, it was calculated with the two-level model.

## 
## Rank Correlation Test for Funnel Plot Asymmetry
## 
## Kendall's tau = 0.1731, p = 0.1484

The p-value is > 0.05, which indicates non-existence of publication bias.

Outlier & influence analysis

Hat values

The hat values are the fitted values, the predictions made by the model for each observation.

##          1          2          3          4          5          6          7 
## 0.02570633 0.02728570 0.02716063 0.02719011 0.02670611 0.02703940 0.02708251 
##          8          9         10         11         12         13         14 
## 0.02929797 0.02927713 0.02931434 0.02810648 0.02886847 0.02839469 0.02596490 
##         15         16         17         18         19         20         21 
## 0.02717960 0.02718419 0.02697977 0.02922146 0.02930504 0.02928871 0.02933955 
##         22         23         24         25         26         27         28 
## 0.02922106 0.02934942 0.02893951 0.02959745 0.02980240 0.02991593 0.02991766 
##         29         30         31         32         33         34         35 
## 0.02934960 0.02952701 0.02936674 0.02941902 0.02987211 0.02989404 0.02993496

Model without Outliers on effectsize level

Two-Level Model without Outliers on effectsize level

Removal of Outliers

Build a two-level model whose robustness then can be compared to the three-level model.

## 
## Random-Effects Model (k = 30; tau^2 estimator: REML)
## 
## tau^2 (estimated amount of total heterogeneity): 0.083 (SE = 0.040)
## tau (square root of estimated tau^2 value):      0.288
## I^2 (total heterogeneity / total variability):   56.02%
## H^2 (total variability / sampling variability):  2.27
## 
## Test for Heterogeneity:
## Q(df = 29) = 66.313, p-val < .001
## 
## Model Results:
## 
## estimate     se   zval   pval  ci.lb  ci.ub 
##    0.391  0.071  5.471  <.001  0.251  0.531  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##        estimate  ci.lb  ci.ub 
## tau^2     0.083  0.029  0.223 
## tau       0.288  0.171  0.472 
## I^2(%)   56.024 31.098 77.438 
## H^2       2.274  1.451  4.432

Three-Level Model without Outliers

Intercept-Only Model

Estimate the overall effect by fitting an intercept-only model.

Request a print of the results stored in the object ‘‘overall’’ in three digits.

## 
## Multivariate Meta-Analysis Model (k = 30; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -14.708    29.416    35.416    39.518    36.376   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.083  0.288     30     no  effectsize_id 
## sigma^2.2  0.000  0.000      9     no       study_id 
## 
## Test for Heterogeneity:
## Q(df = 29) = 66.313, p-val < .001
## 
## Model Results:
## 
## estimate     se   tval   pval  ci.lb  ci.ub 
##    0.391  0.071  5.471  <.001  0.245  0.537  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Variance Distribution

Determine how the total variance is distributed over the three levels of the meta-analytic model. Print the results in percentages on screen.

## [1] 43.97589
## [1] 56.02411
## [1] 0.0000002139203
##         % of total variance    I2
## Level 1    43.9758852554402   ---
## Level 2    56.0241145306396 56.02
## Level 3     0.0000002139203     0
## Total I2: 56.02%

Profile Likelihood Plots

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## 
##           estimate  ci.lb  ci.ub 
## sigma^2.1   0.0827 0.0221 0.2015 
## sigma.1     0.2876 0.1487 0.4489 
## 
##           estimate  ci.lb  ci.ub 
## sigma^2.2   0.0000 0.0000 0.1478 
## sigma.2     0.0000 0.0000 0.3845

Calculation of Intraclass Coefficient

## [1] 0

Total sum of heterogeneity

## [1] 0.083

Residuals

Two-Level Model without within-study variance

Build a two-level model without within-study variance.

Request a print of the results stored in the object # ‘‘movelnovar2_wo’’ in three digits.

## 
## Multivariate Meta-Analysis Model (k = 30; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -20.150    40.301    44.301    47.035    44.762   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.000  0.000     30    yes  effectsize_id 
## sigma^2.2  0.032  0.180      9     no       study_id 
## 
## Test for Heterogeneity:
## Q(df = 29) = 66.313, p-val < .001
## 
## Model Results:
## 
## estimate     se   tval   pval  ci.lb  ci.ub 
##    0.382  0.080  4.791  <.001  0.219  0.545  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Perform a likelihood-ratio-test to determine the significance of the within-study (level2) variance.

## 
##         df     AIC     BIC    AICc   logLik     LRT   pval      QE 
## Full     3 35.4161 39.5180 36.3761 -14.7081                66.3129 
## Reduced  2 44.3008 47.0353 44.7623 -20.1504 10.8846 0.0010 66.3129

Two-Level Model without between-study variance

Build a two-level model without between-study variance

## 
## Multivariate Meta-Analysis Model (k = 30; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -14.708    29.416    33.416    36.151    33.878   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.083  0.288     30     no  effectsize_id 
## sigma^2.2  0.000  0.000      9    yes       study_id 
## 
## Test for Heterogeneity:
## Q(df = 29) = 66.313, p-val < .001
## 
## Model Results:
## 
## estimate     se   tval   pval  ci.lb  ci.ub 
##    0.391  0.071  5.471  <.001  0.245  0.537  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Perform a likelihood-ratio-test to determine the significance of the between-study (level3) variance.

## 
##         df     AIC     BIC    AICc   logLik    LRT   pval      QE 
## Full     3 35.4161 39.5180 36.3761 -14.7081               66.3129 
## Reduced  2 33.4161 36.1507 33.8777 -14.7081 0.0000 1.0000 66.3129

Moderator Analysis

NDT Modality

Determine the potential moderating effect of NDT modality.

Test of different modalities independently.

Acoustic NDT

## 
## Multivariate Meta-Analysis Model (k = 30; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -14.404    28.808    34.808    38.805    35.808   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.085  0.292     30     no  effectsize_id 
## sigma^2.2  0.000  0.000      9    yes       study_id 
## 
## Test for Residual Heterogeneity:
## QE(df = 28) = 64.873, p-val < .001
## 
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 28) = 0.610, p-val = 0.441
## 
## Model Results:
## 
##           estimate     se   tval   pval   ci.lb  ci.ub 
## intrcpt      0.345  0.093  3.714  <.001   0.155  0.536  *** 
## ndt_ayes     0.115  0.147  0.781  0.441  -0.186  0.416      
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Manual NDT

## 
## Multivariate Meta-Analysis Model (k = 30; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -14.097    28.194    34.194    38.191    35.194   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.081  0.285     30     no  effectsize_id 
## sigma^2.2  0.000  0.000      9    yes       study_id 
## 
## Test for Residual Heterogeneity:
## QE(df = 28) = 63.156, p-val < .001
## 
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 28) = 1.221, p-val = 0.279
## 
## Model Results:
## 
##           estimate     se    tval   pval   ci.lb  ci.ub 
## intrcpt      0.432  0.080   5.377  <.001   0.267  0.597  *** 
## ndt_myes    -0.191  0.172  -1.105  0.279  -0.544  0.163      
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Cognitive NDT

## 
## Multivariate Meta-Analysis Model (k = 30; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -14.551    29.101    35.101    39.098    36.101   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.087  0.295     30     no  effectsize_id 
## sigma^2.2  0.000  0.000      9    yes       study_id 
## 
## Test for Residual Heterogeneity:
## QE(df = 28) = 65.911, p-val < .001
## 
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 28) = 0.257, p-val = 0.616
## 
## Model Results:
## 
##           estimate     se   tval   pval   ci.lb  ci.ub 
## intrcpt      0.368  0.086  4.277  <.001   0.192  0.544  *** 
## ndt_cyes     0.081  0.160  0.507  0.616  -0.247  0.409      
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Handheld NDT

## 
## Multivariate Meta-Analysis Model (k = 30; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -13.979    27.958    33.958    37.955    34.958   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.082  0.286     30     no  effectsize_id 
## sigma^2.2  0.000  0.000      9    yes       study_id 
## 
## Test for Residual Heterogeneity:
## QE(df = 28) = 63.148, p-val < .001
## 
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 28) = 1.548, p-val = 0.224
## 
## Model Results:
## 
##          estimate     se    tval   pval   ci.lb  ci.ub 
## intrcpt     0.437  0.080   5.447  <.001   0.272  0.601  *** 
## handyes    -0.217  0.174  -1.244  0.224  -0.573  0.140      
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

All modalities in one model.

## 
## Multivariate Meta-Analysis Model (k = 30; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -13.715    27.430    39.430    46.743    44.097   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.097  0.311     30     no  effectsize_id 
## sigma^2.2  0.000  0.000      9    yes       study_id 
## 
## Test for Residual Heterogeneity:
## QE(df = 25) = 61.580, p-val < .001
## 
## Test of Moderators (coefficients 2:5):
## F(df1 = 4, df2 = 25) = 0.474, p-val = 0.754
## 
## Model Results:
## 
##           estimate     se    tval   pval   ci.lb  ci.ub 
## intrcpt      0.422  0.123   3.425  0.002   0.168  0.675  ** 
## ndt_ayes     0.128  0.261   0.492  0.627  -0.409  0.666     
## ndt_myes    -0.061  0.236  -0.260  0.797  -0.547  0.424     
## ndt_cyes    -0.100  0.275  -0.365  0.718  -0.666  0.465     
## handyes     -0.185  0.228  -0.809  0.426  -0.654  0.285     
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Urgency

One-hot encoding of hand-coded urgency

Determine the potential moderating effect of hand-coded urgency as categorical moderator. No urgency is chosen as the reference category

## 
## Multivariate Meta-Analysis Model (k = 30; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -14.416    28.832    36.832    42.015    38.650   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.090  0.300     30     no  effectsize_id 
## sigma^2.2  0.000  0.000      9    yes       study_id 
## 
## Test for Residual Heterogeneity:
## QE(df = 27) = 64.017, p-val < .001
## 
## Test of Moderators (coefficients 2:3):
## F(df1 = 2, df2 = 27) = 0.373, p-val = 0.692
## 
## Model Results:
## 
##             estimate     se   tval   pval   ci.lb  ci.ub 
## intrcpt        0.348  0.190  1.837  0.077  -0.041  0.738  . 
## urg_medium     0.177  0.256  0.690  0.496  -0.349  0.702    
## urg_high       0.016  0.210  0.077  0.939  -0.414  0.446    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Determine the potential moderating effect of urgency as continuous moderator. High urgency is chosen as inttercept category

## 
## Multivariate Meta-Analysis Model (k = 30; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -14.416    28.832    36.832    42.015    38.650   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.090  0.300     30     no  effectsize_id 
## sigma^2.2  0.000  0.000      9    yes       study_id 
## 
## Test for Residual Heterogeneity:
## QE(df = 27) = 64.017, p-val < .001
## 
## Test of Moderators (coefficients 2:3):
## F(df1 = 2, df2 = 27) = 0.373, p-val = 0.692
## 
## Model Results:
## 
##            estimate     se    tval   pval   ci.lb  ci.ub 
## intrcpt       0.365  0.089   4.082  <.001   0.181  0.548  *** 
## urglow       -0.016  0.210  -0.077  0.939  -0.446  0.414      
## urgmedium     0.160  0.194   0.828  0.415  -0.237  0.558      
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Determine the potential moderating effect of time budget to collision.

## 
## Multivariate Meta-Analysis Model (k = 30; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -14.770    29.539    35.539    39.536    36.539   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.089  0.298     30     no  effectsize_id 
## sigma^2.2  0.000  0.000      9    yes       study_id 
## 
## Test for Residual Heterogeneity:
## QE(df = 28) = 66.238, p-val < .001
## 
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 28) = 0.005, p-val = 0.944
## 
## Model Results:
## 
##          estimate     se   tval   pval   ci.lb  ci.ub 
## intrcpt     0.383  0.143  2.675  0.012   0.090  0.676  * 
## tbtc        0.001  0.014  0.070  0.944  -0.028  0.030    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Further Moderator Analyses

Simulator fidelity

## 
## Multivariate Meta-Analysis Model (k = 30; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -12.745    25.489    33.489    38.672    35.307   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.071  0.267     30     no  effectsize_id 
## sigma^2.2  0.000  0.000      9    yes       study_id 
## 
## Test for Residual Heterogeneity:
## QE(df = 27) = 57.327, p-val < .001
## 
## Test of Moderators (coefficients 2:3):
## F(df1 = 2, df2 = 27) = 2.148, p-val = 0.136
## 
## Model Results:
## 
##                     estimate     se    tval   pval   ci.lb  ci.ub 
## intrcpt                0.840  0.270   3.113  0.004   0.286  1.393  ** 
## simlow fidelity       -0.315  0.314  -1.003  0.325  -0.959  0.329     
## simmedium fidelity    -0.521  0.281  -1.853  0.075  -1.098  0.056   . 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Interaction with other road users

## 
## Multivariate Meta-Analysis Model (k = 30; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -15.639    31.278    39.278    44.606    41.017   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.000  0.000     30     no  effectsize_id 
## sigma^2.2  0.000  0.000      9     no       study_id 
## 
## Test for Residual Heterogeneity:
## QE(df = 28) = 16.990, p-val = 0.949
## 
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 28) = 0.704, p-val = 0.408
## 
## Model Results:
## 
##          estimate     se    tval   pval   ci.lb  ci.ub 
## intrcpt     0.478  0.141   3.393  0.002   0.189  0.766  ** 
## iruyes     -0.157  0.187  -0.839  0.408  -0.541  0.227     
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Level of automated driving

## 
## Multivariate Meta-Analysis Model (k = 30; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -15.931    31.862    39.862    45.191    41.601   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.000  0.000     30     no  effectsize_id 
## sigma^2.2  0.000  0.000      9     no       study_id 
## 
## Test for Residual Heterogeneity:
## QE(df = 28) = 17.467, p-val = 0.939
## 
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 28) = 0.227, p-val = 0.638
## 
## Model Results:
## 
##          estimate     se   tval   pval   ci.lb  ci.ub 
## intrcpt     0.317  0.177  1.789  0.084  -0.046  0.680  . 
## lad1        0.099  0.208  0.476  0.638  -0.327  0.526    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Publication Bias

Visualization: Funnel Plot

Trim-and-fill method

## 
## Estimated number of missing studies on the left side: 4 (SE = 3.6206)
## 
## Random-Effects Model (k = 34; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
## -21.0215   42.0430   46.0430   49.0360   46.4430   
## 
## tau^2 (estimated amount of total heterogeneity): 0.1233 (SE = 0.0481)
## tau (square root of estimated tau^2 value):      0.3512
## I^2 (total heterogeneity / total variability):   64.74%
## H^2 (total variability / sampling variability):  2.84
## 
## Test for Heterogeneity:
## Q(df = 33) = 91.1965, p-val < .0001
## 
## Model Results:
## 
## estimate      se    zval    pval   ci.lb   ci.ub 
##   0.3120  0.0763  4.0904  <.0001  0.1625  0.4615  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Egger Regression Symmetry Test (eggers.test not working, bc ‘overall’ is no ‘meta’-type. Regtest is carried out with the two-level model)

## 
## Regression Test for Funnel Plot Asymmetry
## 
## model:     mixed-effects meta-regression model
## predictor: standard error
## 
## test for funnel plot asymmetry: z = 0.7768, p = 0.4373

The p-value is > 0.05, publication bias can be rejected.

Another method for calculating Egger’s regression test - same result though.

## 
## Multivariate Meta-Analysis Model (k = 30; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -14.349    28.698    36.698    42.027    38.437   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.000  0.000      9     no       study_id 
## sigma^2.2  0.083  0.289     30     no  effectsize_id 
## 
## Test for Residual Heterogeneity:
## QE(df = 28) = 64.368, p-val < .001
## 
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 28) = 0.603, p-val = 0.444
## 
## Model Results:
## 
##          estimate     se   tval   pval   ci.lb  ci.ub 
## intrcpt     0.127  0.347  0.366  0.717  -0.584  0.838    
## mods        1.017  1.309  0.777  0.444  -1.664  3.697    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Rank-Correlation Test

## 
## Rank Correlation Test for Funnel Plot Asymmetry
## 
## Kendall's tau = 0.2046, p = 0.1170

Model without Lin et al., 2020

Two-Level Model without Lin et al., 2020

Removal of Outliers

Build a two-level model whose robustness then can be compared to the three-level model.

## 
## Random-Effects Model (k = 29; tau^2 estimator: REML)
## 
## tau^2 (estimated amount of total heterogeneity): 0.422 (SE = 0.134)
## tau (square root of estimated tau^2 value):      0.649
## I^2 (total heterogeneity / total variability):   85.62%
## H^2 (total variability / sampling variability):  6.96
## 
## Test for Heterogeneity:
## Q(df = 28) = 150.829, p-val < .001
## 
## Model Results:
## 
## estimate     se   zval   pval  ci.lb  ci.ub 
##    0.433  0.132  3.289  0.001  0.175  0.691  ** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##        estimate  ci.lb  ci.ub 
## tau^2     0.422  0.246  0.936 
## tau       0.649  0.496  0.967 
## I^2(%)   85.623 77.679 92.966 
## H^2       6.956  4.480 14.217

Three-Level-Model without Lin et al., 2020

Intercept-Only Model

Estimate the overall effect by fitting an intercept-only model.

Request a print of the results stored in the object ‘‘overall’’ in three digits.

## 
## Multivariate Meta-Analysis Model (k = 29; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -31.095    62.191    68.191    72.187    69.191   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.422  0.649     29     no  effectsize_id 
## sigma^2.2  0.000  0.000      8     no       study_id 
## 
## Test for Heterogeneity:
## Q(df = 28) = 150.829, p-val < .001
## 
## Model Results:
## 
## estimate     se   tval   pval  ci.lb  ci.ub 
##    0.433  0.132  3.289  0.003  0.163  0.703  ** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Variance Distribution

Determine how the total variance is distributed over the three levels of the meta-analytic model. Print the results in percentages on screen.

## [1] 14.37685
## [1] 85.62315
## [1] 0.00000005084847
##         % of total variance    I2
## Level 1   14.37684599661965   ---
## Level 2   85.62315395253188 85.62
## Level 3    0.00000005084847     0
## Total I2: 85.62%

Profile Likelihood Plots

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## 
##           estimate  ci.lb  ci.ub 
## sigma^2.1   0.4216 0.2168 0.8389 
## sigma.1     0.6493 0.4656 0.9159 
## 
##           estimate  ci.lb  ci.ub 
## sigma^2.2   0.0000 0.0000 0.1884 
## sigma.2     0.0000 0.0000 0.4341

Calculation of Intraclass Coefficient

## [1] 0

Total sum of heterogeneity

## [1] 0.422

Residuals

Two-Level Model without within-study variance

Build a two-level model without within-study variance.

Request a print of the results stored in the object # ‘‘movelnovar2’’ in three digits.

## 
## Multivariate Meta-Analysis Model (k = 29; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -64.941   129.882   133.882   136.547   134.362   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.000  0.000     29    yes  effectsize_id 
## sigma^2.2  0.013  0.114      8     no       study_id 
## 
## Test for Heterogeneity:
## Q(df = 28) = 150.829, p-val < .001
## 
## Model Results:
## 
## estimate     se   tval   pval  ci.lb  ci.ub 
##    0.390  0.066  5.868  <.001  0.254  0.526  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Perform a likelihood-ratio-test to determine the significance of the within-study (level2) variance.

## 
##         df      AIC      BIC     AICc   logLik     LRT   pval       QE 
## Full     3  68.1908  72.1874  69.1908 -31.0954                150.8287 
## Reduced  2 133.8823 136.5467 134.3623 -64.9412 67.6915 <.0001 150.8287

Two-Level Model without between-study variance

Build a two-level model without between-study variance

## 
## Multivariate Meta-Analysis Model (k = 29; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -31.095    62.191    66.191    68.855    66.671   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.422  0.649     29     no  effectsize_id 
## sigma^2.2  0.000  0.000      8    yes       study_id 
## 
## Test for Heterogeneity:
## Q(df = 28) = 150.829, p-val < .001
## 
## Model Results:
## 
## estimate     se   tval   pval  ci.lb  ci.ub 
##    0.433  0.132  3.289  0.003  0.163  0.703  ** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Perform a likelihood-ratio-test to determine the significance of the between-study (level3) variance.

## 
##         df     AIC     BIC    AICc   logLik    LRT   pval       QE 
## Full     3 68.1908 72.1874 69.1908 -31.0954               150.8287 
## Reduced  2 66.1908 68.8552 66.6708 -31.0954 0.0000 1.0000 150.8287

Moderator Analysis

NDT Modality

Determine the potential moderating effect of ndt modality.

Test of different modalities independently

## 
## Multivariate Meta-Analysis Model (k = 30; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -14.404    28.808    34.808    38.805    35.808   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.085  0.292     30     no  effectsize_id 
## sigma^2.2  0.000  0.000      9    yes       study_id 
## 
## Test for Residual Heterogeneity:
## QE(df = 28) = 64.873, p-val < .001
## 
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 28) = 0.610, p-val = 0.441
## 
## Model Results:
## 
##           estimate     se   tval   pval   ci.lb  ci.ub 
## intrcpt      0.345  0.093  3.714  <.001   0.155  0.536  *** 
## ndt_ayes     0.115  0.147  0.781  0.441  -0.186  0.416      
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

— manual

## 
## Multivariate Meta-Analysis Model (k = 29; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -30.283    60.565    66.565    70.453    67.609   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.437  0.661     29     no  effectsize_id 
## sigma^2.2  0.000  0.000      8    yes       study_id 
## 
## Test for Residual Heterogeneity:
## QE(df = 27) = 150.814, p-val < .001
## 
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 27) = 0.440, p-val = 0.513
## 
## Model Results:
## 
##           estimate     se   tval   pval   ci.lb  ci.ub 
## intrcpt      0.380  0.156  2.430  0.022   0.059  0.700  * 
## ndt_myes     0.200  0.301  0.664  0.513  -0.418  0.818    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

— cognitive

## 
## Multivariate Meta-Analysis Model (k = 29; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -30.491    60.981    66.981    70.869    68.025   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.442  0.665     29     no  effectsize_id 
## sigma^2.2  0.000  0.000      8    yes       study_id 
## 
## Test for Residual Heterogeneity:
## QE(df = 27) = 150.647, p-val < .001
## 
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 27) = 0.023, p-val = 0.879
## 
## Model Results:
## 
##           estimate     se   tval   pval   ci.lb  ci.ub 
## intrcpt      0.419  0.165  2.546  0.017   0.081  0.757  * 
## ndt_cyes     0.044  0.285  0.153  0.879  -0.541  0.628    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

—handheld

## 
## Multivariate Meta-Analysis Model (k = 29; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -30.335    60.669    66.669    70.557    67.713   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.439  0.662     29     no  effectsize_id 
## sigma^2.2  0.000  0.000      8    yes       study_id 
## 
## Test for Residual Heterogeneity:
## QE(df = 27) = 150.826, p-val < .001
## 
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 27) = 0.359, p-val = 0.554
## 
## Model Results:
## 
##          estimate     se   tval   pval   ci.lb  ci.ub 
## intrcpt     0.388  0.154  2.518  0.018   0.072  0.704  * 
## handyes     0.187  0.312  0.599  0.554  -0.453  0.826    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

All modalities in one model

## 
## Multivariate Meta-Analysis Model (k = 29; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -27.622    55.244    67.244    74.312    72.185   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.473  0.688     29     no  effectsize_id 
## sigma^2.2  0.000  0.000      8    yes       study_id 
## 
## Test for Residual Heterogeneity:
## QE(df = 24) = 145.148, p-val < .001
## 
## Test of Moderators (coefficients 2:5):
## F(df1 = 4, df2 = 24) = 0.524, p-val = 0.719
## 
## Model Results:
## 
##           estimate     se    tval   pval   ci.lb  ci.ub 
## intrcpt      0.462  0.280   1.650  0.112  -0.116  1.040    
## ndt_ayes    -0.525  0.460  -1.141  0.265  -1.473  0.424    
## ndt_myes    -0.006  0.431  -0.014  0.989  -0.895  0.884    
## ndt_cyes     0.525  0.449   1.171  0.253  -0.401  1.452    
## handyes      0.197  0.399   0.493  0.627  -0.627  1.021    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Urgency

One-hot encoding of urgency

Determine the potential moderating effect of urgency as categorical moderator. No urgency is chosen as the reference category

## 
## Multivariate Meta-Analysis Model (k = 29; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -29.872    59.743    67.743    72.776    69.648   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.464  0.681     29     no  effectsize_id 
## sigma^2.2  0.000  0.000      8    yes       study_id 
## 
## Test for Residual Heterogeneity:
## QE(df = 26) = 148.978, p-val < .001
## 
## Test of Moderators (coefficients 2:3):
## F(df1 = 2, df2 = 26) = 0.068, p-val = 0.934
## 
## Model Results:
## 
##             estimate     se   tval   pval   ci.lb  ci.ub 
## intrcpt        0.350  0.360  0.974  0.339  -0.389  1.090    
## urg_medium     0.175  0.484  0.363  0.720  -0.819  1.170    
## urg_high       0.077  0.397  0.194  0.848  -0.739  0.892    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Determine the potential moderating effect of urgency as continuous moderator. High urgency is chosen as inttercept category

## 
## Multivariate Meta-Analysis Model (k = 29; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -29.872    59.743    67.743    72.776    69.648   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.464  0.681     29     no  effectsize_id 
## sigma^2.2  0.000  0.000      8    yes       study_id 
## 
## Test for Residual Heterogeneity:
## QE(df = 26) = 148.978, p-val < .001
## 
## Test of Moderators (coefficients 2:3):
## F(df1 = 2, df2 = 26) = 0.068, p-val = 0.934
## 
## Model Results:
## 
##            estimate     se    tval   pval   ci.lb  ci.ub 
## intrcpt       0.427  0.167   2.560  0.017   0.084  0.770  * 
## urglow       -0.077  0.397  -0.194  0.848  -0.892  0.739    
## urgmedium     0.099  0.364   0.271  0.788  -0.649  0.846    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Determine the potential moderating effect of time budget to collision.

## 
## Multivariate Meta-Analysis Model (k = 29; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -30.518    61.035    67.035    70.923    68.079   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.444  0.666     29     no  effectsize_id 
## sigma^2.2  0.000  0.000      8    yes       study_id 
## 
## Test for Residual Heterogeneity:
## QE(df = 27) = 150.829, p-val < .001
## 
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 27) = 0.028, p-val = 0.868
## 
## Model Results:
## 
##          estimate     se    tval   pval   ci.lb  ci.ub 
## intrcpt     0.475  0.281   1.688  0.103  -0.102  1.052    
## tbtc       -0.005  0.028  -0.168  0.868  -0.061  0.052    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Further Moderator Analyses

Simulator fidelity

## 
## Multivariate Meta-Analysis Model (k = 29; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -29.350    58.699    66.699    71.732    68.604   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.446  0.668     29     no  effectsize_id 
## sigma^2.2  0.000  0.000      8    yes       study_id 
## 
## Test for Residual Heterogeneity:
## QE(df = 26) = 147.021, p-val < .001
## 
## Test of Moderators (coefficients 2:3):
## F(df1 = 2, df2 = 26) = 0.567, p-val = 0.574
## 
## Model Results:
## 
##                     estimate     se    tval   pval   ci.lb  ci.ub 
## intrcpt                0.755  0.368   2.051  0.050  -0.002  1.512  . 
## simlow fidelity       -0.229  0.486  -0.472  0.641  -1.229  0.770    
## simmedium fidelity    -0.409  0.403  -1.016  0.319  -1.236  0.419    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Interaction with other road users

## 
## Multivariate Meta-Analysis Model (k = 29; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -29.828    59.657    67.657    72.840    69.475   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.195  0.442     29     no  effectsize_id 
## sigma^2.2  0.000  0.000      8     no       study_id 
## 
## Test for Residual Heterogeneity:
## QE(df = 27) = 48.173, p-val = 0.007
## 
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 27) = 0.193, p-val = 0.664
## 
## Model Results:
## 
##          estimate     se    tval   pval   ci.lb  ci.ub 
## intrcpt     0.487  0.187   2.598  0.015   0.102  0.871  * 
## iruyes     -0.112  0.255  -0.439  0.664  -0.636  0.412    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Level of automated driving

## 
## Multivariate Meta-Analysis Model (k = 29; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -29.831    59.662    67.662    72.845    69.480   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.196  0.443     29     no  effectsize_id 
## sigma^2.2  0.000  0.000      8     no       study_id 
## 
## Test for Residual Heterogeneity:
## QE(df = 27) = 48.097, p-val = 0.007
## 
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 27) = 0.263, p-val = 0.612
## 
## Model Results:
## 
##          estimate     se   tval   pval   ci.lb  ci.ub 
## intrcpt     0.320  0.244  1.311  0.201  -0.181  0.820    
## lad1        0.147  0.286  0.513  0.612  -0.440  0.734    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Publication Bias

Trim-and-fill method

## 
## Estimated number of missing studies on the left side: 7 (SE = 3.5718)
## 
## Random-Effects Model (k = 36; tau^2 estimator: REML)
## 
##   logLik  deviance       AIC       BIC      AICc 
## -46.0221   92.0443   96.0443   99.1549   96.4193   
## 
## tau^2 (estimated amount of total heterogeneity): 0.6845 (SE = 0.1841)
## tau (square root of estimated tau^2 value):      0.8273
## I^2 (total heterogeneity / total variability):   90.23%
## H^2 (total variability / sampling variability):  10.23
## 
## Test for Heterogeneity:
## Q(df = 35) = 259.2019, p-val < .0001
## 
## Model Results:
## 
## estimate      se    zval    pval    ci.lb   ci.ub 
##   0.2021  0.1463  1.3809  0.1673  -0.0847  0.4889    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Egger Regression Symmetry Test

(eggers.test not working, bc ‘overall’ is no ‘meta’-type. Regtest is carried out with the two-level model)

## 
## Regression Test for Funnel Plot Asymmetry
## 
## model:     mixed-effects meta-regression model
## predictor: standard error
## 
## test for funnel plot asymmetry: z = 1.2719, p = 0.2034

The p-value is > 0.05, publication bias can be rejected.

Another method for calculating Egger’s regression test - same result though.

## 
## Multivariate Meta-Analysis Model (k = 29; method: REML)
## 
##   logLik  Deviance       AIC       BIC      AICc 
##  -29.702    59.404    67.404    72.587    69.222   
## 
## Variance Components:
## 
##            estim   sqrt  nlvls  fixed         factor 
## sigma^2.1  0.000  0.000      8     no       study_id 
## sigma^2.2  0.415  0.644     29     no  effectsize_id 
## 
## Test for Residual Heterogeneity:
## QE(df = 27) = 145.893, p-val < .001
## 
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 27) = 1.618, p-val = 0.214
## 
## Model Results:
## 
##          estimate     se    tval   pval   ci.lb  ci.ub 
## intrcpt    -0.358  0.635  -0.563  0.578  -1.660  0.945    
## mods        2.839  2.232   1.272  0.214  -1.741  7.418    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Rank-Correlation Test

## 
## Rank Correlation Test for Funnel Plot Asymmetry
## 
## Kendall's tau = 0.1872, p = 0.1608